What's the fastest way to select every other vertex of an edge ring?
In edit mode with entire edge ring selected: 

Select> Checker Deselect

This should deselect every other vertex.

You can then use the 'offset' value in the toolshelf if you want the other vertices in the edge ring selected.

No Offset:


Offset by 1:


Note: This works in edge and face mode too, deselecting alternate edges or faces to get a checkerboard selection.